You will need an excavator. Many large landscaping companies can propably do it. I have one who handles the western part of Fairfield County not far from Litchfield County. It will not be cheap. I'm speculating 1000's.
If you need further info let me know. Good luck. Also, think first about what value the court adds before removing. You just may have guests who play.You can add a basketball hoop inside the court. Do not know how much acreage you have and what location or space it takes up. Just a thought.
Keller Williams Platinum Properties
Fairfield County, CT